Copernicus studied in the Collegius maius between 1491 and 1495. On the list of 69 students matriculated in 1491 at the Cracok Academy were “Nicolaus Nicolai de Thuronia” and aslso his brother “Andreas Nicolai”. The Jagiellonian University consisted offour faculties at the time (the Theological Faculty, the Canonical La Faculty, the Medical Faculty and the Liberal Arts Faculty). Copernicus began his studies learning the grammar of Latin, poetry and rhetoric but he early started to attend lectures on Euclidean geometry and astronomy. During the 15th and early 16th centuries, the University gained importance in Central Europe as a scientific center due to the high level of astronomical and mathematical sciences: the distinguished professors of the time included Marcin Hrol (c.1422-c.1453), Wojciech of Brudzewo (1445-1495), Jan of Glogow (c.1445-1507) and Maciej of Miechow (1453-1523). In the second semester of 1493 he attended lectures of Jerzy Peürbach, with the comments of Wojciech of Brudzewo, and the lectures about Aristotle’s De Caelo. It’s unknown when Copernicus brothers finished their studies n Cracow but they surely didn’t receive their degrees. Perhaps their mother’s death in 1495 caused their return to Prussia.
Thus one of the required mathematical visits that must be done in Cracow is this College:
The building hosts an interesting museum with a lot of old objects which are not directly related to the College but I must recognize that it’s possible to imagine how the academical life was in the 15th century. The first room is a big hall full of shelves with books, statutes, quadrants, portraits, maps and spheres:
Everything takes you back to a ‘kitsch’ Renaissance:
There is space for our Copernicus, of course,…:
…and also for Galileo:
There is a special small room dedicated exclusively to Copernicus with astrolabes, charts, books and copies of some interesting documents:
For example, look at this interesting torquetum made by Hans Dorn in 1480 (the astrolabe was also made by Dorn in 1486)…:
…or this portrait of Kepler from the 18th century:
Furthermore, a bust of Isaac Newton…
… is on the top of the door through which you enter a room full of astronomical and mathematical instruments:
Can you see this little Aechimedes screw?
Before ending the visit, Newton (again!) says goodgye to the visitors in a very modern picture:
And Kepler too!
One thing more… Go to the ticket office and you will see some mathematical objects more like these English Napier Rods from the 17th century:
Location: Collegius Maius (map)
In a previous post I began to talk about this museum located inside Frombork castle. You can learn almost everything about him, his life and his works on medicine, economies and, of course, astronomy, including the replicas of his instruments (we saw them also in Warsaw). For example, it’s possible to see some facsmile editions of his works and also a recreation of his desk:
Among the references about his publication of his works, we can find this engraving showing Copernicus in a lecture for the Cracovian scientists in 1509:
Or this other wonderful one (1873) with Copernicus in he middle of the picture talking about his heliocentric system:
How proud he is of his heliocentric theory!
And who are his guests? First of all, Hipparcus (with the armillar spher) and Ptolemy (with his geocentric system) are listening the theory which will finish theirs. Ptolemy looks askance at Tycho Brahe meanwhile Newton is looking at Laplace:
Galileo Galilei is behind Copernicus looking at him with great reverence:
And Hevelius, the other great Polish astronomer, agrees Copernicus’ theories although he never had the telescope to check them.
Finally, Johannes Kepler seems to be bored of listening this obvious theory although his ellipses will be the curves which will change the astronomy.
A beautiful picture for a beautiful museum. Next step: the cathedral!
Location: Frombork castle (map)
This is one of the Top 10 Museums in Prague! The museum was founded in 1908 and has been in its current location since 1941. It’s a very big building and the collection exhibited is so big although the exhibition about transports is its main attraction:
But for me, the exhibition about Astronomy has been the interesting part of the museum and I have been able to visit it on my own meanwhile my children were playing in another room with some technical toys. The astronomical rooms are very dark so it has been very difficult to take good pictures although I’ve tried to do my best. The collections has sundials, armilar spheres, quadrants, astrolabes,… and a lot of other astronomical instruments:
For example, the polyhedrical sundials are so beautiful like this constructed on a cube by German David Beringer around 1750:
Or… what about this other constructed by Mathias Karl Krausler in 1691?
The oldest exhibited astrolabe is this unsigned one from around 1450:
And there also is an unsigned torquetum from the late 16th century:
One of the instruments which have surprised me has been Joost Bürgi’s sextant for measuring the angles of celestial bodies (I knew that Bürgi, one of the inventor of logarithms, had constructed a lot of clocks and astronomical instruments but I didn’t expect to find one here!). Kepler used it to measure two consecutive oppositions of the planet Mars in 1602 and 1604.
There also is Habermel’s sextant, built by Erasmus Habermel (1538 – 15th of November of 1606 in Prag) who was mechanic at the court of Emperor Rudolph II:
The prevailing opinion for a long time was that the instrument belonged to Brahe and so it was called the “Tychonian sextant”.
Habermel was specialised in small devices and portable sundials and one example is this sundial in the form of a book (c.1600)…
… and another is this equinoctial sundial (1585):
Finally, look at this armilar sphere from the second half of the 16th century! It’s a piece of art!
The first object which you can see in the second floor of the Pergamon Museum in Berlin is this Iraqi astrolabe made by the astronomer and poet Hibât Allâh al-Bagdâdî and designed by the great Abû Jacfâr al-Khâzin (c.900-c.970). This bronze piece is unique!
Al-Khâzin was a very important Persian mathematician and astronomer who worked in Ray and wrote a Commentary on the Almagest. He also wrote one of the most important work on the construction of astrolabes which was very appreciated by his colleagues.
Location: Pergamon Museum (map)
This post is about a very interesting exhibition about 26 selected scientific books which I visited in Madrid in August and it can be visited now in A Coruña (from the 17th October). There are explanation of the 26 books and their authors and I am going to talk about the mathematical ones (of course!). Furthermore, there are Eulogia Merle‘s drawings of every scientist exhibited here so this is another interesting attraction to visit it.
The first great mathematician is Euclid (c.295 BC).
[In Spanish:] Es difícil precisar datos de la biografía del más destacado matemático de la antigüedad grecolatina, considerado el Padre de la Geometría. Solo se conocen con certeza dos hechos indiscutibles: vivió en una época intermedia entre los discípulos de Platón y los de Arquímedes, y formó una gran escuela de matemáticas en Alejandría. Según el filósofo bizantino Proclo, Euclides enseñó en esta ciudad del delta del Nilo durante el mandato de Ptolomeo I Sóter, es decir, entre los años 323 y 285 a.C. Murió en torno al año 270 a.C. Su fama radica en ser el autor de los Elementos, un tratado de geometría que ha servido de libro de tecto en la materia hasta comienzo del siglo XX. Está compuesto por trece libros que tratatn de geometría en dos y tres dimensiones, proporciones y teoría de números. Presenta toda la geometría basándose en teoremas que pueden derivarse a partir de cinco axiomas o postulados muy simples que se aceptan como verdaderos.
There are two different digital editions of the Elements and a compass from the 16th or 17th century with all this information:
The next Greek mathematician is Archimedes (287-212 BC) although his book here is On the floating bodies which is less mathematical than phisician.
Ptolemy (2nd century) is the next and his Almagest was the most important astronomical book since the 16th century.
There is also an interesting wooden astrolabe from 1630 (“Claudii Ricchardi”):
Arsitotle, Hippocrates and Pliny the Younger are the other three Greek scientists represented in the exhibition.
The collection of astrolabes is very interesting and there are pieces from the 14th to the 19th century.
For example, look at this English astrolabe from the 14th century:
One of the most interesting objects of the exhibition is this Egyptian sundial from the 1st to 3rd century AD (Roman Imperial date):
Sundial construction requires expert knowledge of the apparent movement of the Sun, both in its daily and annual motion. Hence the construction of sundials has often been considered part of astronomy.
The diagram that represents annual motion is called the ‘analemma’ and was known in classical antiquity. Many different designs of sundial can be derived from the analemma. This dial has two scales, one for the morning, one for the afternoon; the shadow is cast by the prominence between them.
Of course there are more sundials like this pillar dial made in 1542 and this ring dial made in 1588…
… or all these different dials of different kinds, epochs and countries:
Upstairs there is a replica of an antique globe fragment which is on display in the Neues Museum:
The Whipple is a University of Cambridge museum within the Department of History and Philosophy of Science. During the 1930s and 1940s, there were strong initiatives to establish history of science within the University and an exhibition of the historical scientific apparatus owned by various colleges was held in 1936. Soon after, a History of Science Lectures Comittee was established which, together with the Cambridge Philosophical Society, negotiated in 1944 a donation of antique scientific instruments and rare books from Robert Stewart Whipple (1871-1953), former Director of the Cambridge Scientific Instrument Company.
So, let’s start our visit in the main room:
The astronomical objects are very usual in this kind of museums and here you have a Newtonian “Herschdel Telescope” (c.1790) which was presented by George III to the Duke of Marlborough and it was placed in the Observatory at Blenheim Palace until it was given to Herschel’s great-grandson, Mr. Joseph A. Hardcastle (1816-1911).
Sir William Herschel achieved public acclaim and royal favour through his discovery of the planet Uranus, which he originally called Georgium Sidus, to honour King George III in 1781. A few years later George III requested that he make a number of telescopes. This is one of five 10-ft reflecting telescopes made in response to that request. Following Herschel’s standard design, the King’s cabinet-maker constructed the mahogany stand and tube. Herschdel made the optical parts himself.
There also are polyhedral sundials, more telescopes, astrolabes,…
… and this wonderful planetarium made by George Adams around 1750.
This grand Orrery, which is not to scale, displays the Sun in the centre, and the 6 then known planets and their satellites; 4 around Jupiter and 5 around Saturn. The planets Uranus, Neptune and Pluto had not yet been discovered.
Now, let’s teke a look at the collection of astrolabes and sundials but… it will be done in the next post!
The National Maritime Museum is another of the touristic attractions which can be visited in Greenwich. Of course, you can see boats, ships, maps,… and all the things related to the sea and the English glorious past. Therefore… what can the mathematical tourist visit here? Navigators used charts, maps, astrolabes, globes,… in their adventures so we can start our mathematical visit with all these mathematical objects!
Brass celestial globe. German, about 1725
This is one of a pair with a terrestial globe. It shows constellations, the Milky Way and the Magellanic Clouds. It contains some mistakes, indicating that it was a luxury item that could adorna wealthy home rather than an up-to-date scientific instrument. Nevertheless, with its calendar ring, it could be used to identify what was seen in the night sky.
There also are terrestial globes which were used by navigators to measure distances on the terrestial surfaces:
The first golden globe is from 1600 and the globe at its right is a French globe from 1625. Behind it there is a German terrestial globe by Johann Reinhold (1588). Of course, sundials also are shown in the exhibition! The first one (left) is an inclining dial for use in Japan before 1872 and the second is an equinoctial dial fou use in Huangzou, China, in the 19th century:
We can also find astrolabes, compasses, quadrants, telescopes, rulers,…
Look at this astrolabe from Islamic Spain (c.1230) by an unknown maker! It’s a jewel!
I am sure that you can find out more mathematical objects if you have enough time to enjoy all the exhibition!
This is the famous Royal Game of Ur (2600-2300 BC). This wooden game board was in at least six graves in the Royal Cemetery so it’s an early example of a game that was played all over the ancient Near East for about 3.000 years.
The game is a race for two players using dice with seven identical pieces each. All playing squares are decorated, but on later boards only the five ‘rosette’ squares are marked. […] Pieces are ‘at war’ along the central path but turn off to their own side to exit.
Playing pieces were discs of shell or lapis lazuli. The tetrahedrical dice of the game are also exhibited.
Apart of the Royal Game of Ur, the only exhibited objects which are related with Mespotamian mathematics are the Archaic and Cuneiform tablets. For example, look at this tablet containing a five day ration list (Jemdet Nasr, 3000-2900 BC):
Each line contains rations for one day and the sign for ‘day’ and numbers 1, 2, 3, 4 and 5 are easily identificable (at the beginning of the line!).
This Gypsum tablet with Archaic numbers (Uruk, 3300 BC) has 3 units (round impressions) and 3 ‘tens’ (elongated impressions).
This tablet above contains the daily barley beer ration for the workers (3300-3100 BC). Here there are also identificable all the marks representing units and tens and it’s the same in the next tablet containig food rations (3300-3100 BC):
Finally, there is another tablet from the Late Uruk Period (3300-3100 BC):
However, mathematical tables are not only clay tablets with figures and numbers. For example, the next tablet contains a set of problems relating to the calculation of volume, together with the solutions.
You can see the details of the tablet in the next two pictures:
There is also a tablet recording observations of the planet Venus from c.1700 BC:
Astronomical tablets were so common in Mesopotamia and here we have a representation of the heavens in eight segments which include drawings of the constellations.
The next piece of cuneiform tablet contains a star chart which was found in Ashurbanipal’s library:
According the British Museum’s web…
Ashurbanipal, whose name (Ashur-bani-apli) means, ‘the god Ashur is the creator of the heir’, came to the Assyrian throne in 668 BC. He continued to live in the Southwest Palace of his grandfather, Sennacherib, in Nineveh, which he decorated with wall reliefs depicting his military activity in Elam. He also had a new residence built at Nineveh, known today as the North Palace. The famous lion hunt reliefs, some of which are now in The British Museum, formed part of the new palace’s decorative scheme.
Throughout his reign, Ashurbanipal had military problems, mainly at the borders of the empire. He also continued his father’s policy of attacking Egypt. Campaigns in 667 and 664 BC led to the defeat of the Egyptian Twenty-fifth Dynasty and the appointment of a pro-Assyrian ruler in the Nile Delta. Assyria also attacked Elam, possibly in 658-57 BC, following the receipt of insulting letters from the Elamite king. In 652 BC Shamash-shum-ukin, Ashurbanipal’s brother, and ruler of Babylonia, revolted against Assyria with the support of the Elamites. The Assyrian army invaded Elam and Babylonia. Babylon was captured in 648 BC and the following year the Elamite city of Susa was destroyed. There is little surviving evidence that can help us to reconstruct the last years of Ashurbanipal’s reign. Ashurbanipal boasted of his ability to read the cuneiform script, and was responsible for the collection and copying of a major library of contemporary literary and religious texts
I visited the Museum of the History of Science of Oxford last 6th of August and it was one of the best moments in my Holidays. The MUSEUM (in capital letters!) is not so big but it’s so interesting for a person like me and I am going to write some post about it and its collections. However, there is no picture which can show the essence of such a wonderful collection!
I am going to start with some of the astrolabes:
In this picture you can see some interesting astrolabes from different epochs, as for example:
Astrolabe by Muhammad Tahir, Persian, c. 1710
Astrolabe by Muhammad Salih Tatawi, Indo-Persian, 1666/7
Three of the other six astrolabes of this showcase were made by ‘Abd al-A’imma (Persia, early 18th century), another by Shams al-Din Muhammad Saffar (Persia, 1481/2), another by Muhammad Mahdi al-Yazdi (Persia, c.1660), and there is one more from an anonymus astronomer from the 15th or 16th century.
The collection of astrolabes is much greater upstairs where we can find more of them:
Two unsigned Flemish astrolabes. It is still something of a puzzle that many early instruments were not signed by their makers although the more usual practice was to include a signature.
The first astrolabe is attributed to Michael Coignet and the astrolabe behind this has many characteristics of the instruments produced in the workshop begun in Louvain by Gemma Frisius.
Shall we continue? In the Lewis Evans Collection we find (for example) the next Italian 16yh-century astrolabe:
and this Hispano-Moorish one from 1221:
The signature on this astrolabe reads, “In the name of God. Made by Muhammad ibn Fattuh al-Khama’iri in the city of Seville in the year 618 of the Hijra”.
It’s impossible to reproduce all the asrolabes of the museum and perhaps you shouls buy the catalog if you are interested in the. Here you have some Persian astroalber from the 17th and 18th centuries: